Which of the following may be true?

Question

If m=121-5k is divisible by 3, which of the following may be true?

 

I. m is odd

II. m is even

III. k is divisible by 3

Answer 1

m = 121 - 5(2) = 111 which is divisible by 3

 

So, m can be odd

 

m = 121 - 5(5) = 96 which is divisible by 3

 

So, m could be even

 

If k is divisible by 3, then k = 3a, for some integer, a

 

So, m = 121 - 15a.  But, m is divisible by 3, so m = 3b, for some integer, b

 

   We would then have 121 - 15a = 3b

 

                                121 = 15a + 3b = 3(5a+b)

 

                                So, 121 is divisible by 3, which is obviously false

 

Thus, the assumption that k is divisible by 3 is untrue.

 

Statements I and II are possible, but III is not possible.   

 

                                

 

 

Answer 2

3|m=11²-5k  Let m=3n

11²-3n=5k

121-3×2=115=5×23    m=6, k=23

121-3×7=100=5×20   m=21, k=20

121-3×12=85=5×17   m=36, k=17

121-3×17=70=5×14   m=51, k=14

121-3×22=55=5×11   m=66, k=11

121-3×27=40=5×8    m=81, k=8

121-3×32=25=5×5    m=96, k=5

121-3×37=10=5×2   m=111, k=2

are all possible solutions.  You may read the properties needed.

Answer 3

I. and II.

K value starts at 2, and moves in increments of 3. (2,5,8,11,14...)

Because K moves in increments of 3, the value switches from even to odd the entire time. If K keeps changing values, m will to.

Because K moves in increments of 3, but started at 2, it cannot be divided evenly by three.